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normed

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The answer NORMED has 0 possible clue(s) in existing crosswords.

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Definitions of normed in various dictionaries:

adj - having a norm

NORMED - In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined. A norm is the formalization and...

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Possible Dictionary Clues
adjust (something) to conform to a norm.
(analysis) Of a mathematical structure, endowed with a norm.
Of a data set that has been adjusted to a norm.

Normed description
In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined. A norm is the formalization and the generalization to real vector spaces of the intuitive notion of distance in the real world. A norm is a real-valued function defined on the vector space that has the following properties:* The zero vector, 0, has zero length; every other vector has a positive length. * * * * * ‖ * x * ‖ * ≥ * 0 * * * {\displaystyle \\|x\\|\geq 0} * , and * * * * ‖ * x * ‖ * = * 0 * * * {\displaystyle \\|x\\|=0} * if and only if * * * * x * = * 0 * * * {\displaystyle x=0} * * Multiplying a vector by a positive number changes its length without changing its direction. Moreover, * * * * ‖ * α * x * ‖ * = * * \| * * α * * \| * * ‖ * x * ‖ * * * {\displaystyle \\|\alpha x\\|=\|\alpha \|\\|x\\|} * for any scalar * * * * α * . * * * {\displaystyle \alpha .} * * The triangle inequality holds. That is, taking norms as distances, the distance from point A through B to C is never shorter than going directly from A to C, or the shortest distance between any two points is a straight line. * * * * * ‖ * x * + * y * ‖ * ≤ * ‖ * x * ‖ * + * ‖ * y * ‖ * * * {\displaystyle \\|x+y\\|\leq \\|x\\|+\\|y\\|} * for any vectors x and y. (triangle inequality)The generalization of these three properties to more abstract vector spaces leads to the notion of norm. A vector space on which a norm is defined is then called a normed space or normed vector space. * Normed vector spaces are central to the study of linear algebra and functional analysis.

Normed description

In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined. A norm is the formalization and the generalization to real vector spaces of the intuitive notion of distance in the real world. A norm is a real-valued function defined on the vector space that has the following properties:* The zero vector, 0, has zero length; every other vector has a positive length.
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* for any vectors x and y. (triangle inequality)The generalization of these three properties to more abstract vector spaces leads to the notion of norm. A vector space on which a norm is defined is then called a normed space or normed vector space.
* Normed vector spaces are central to the study of linear algebra and functional analysis.

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